Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-6y &= -3 \\ -7x-6y &= -3\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-6y = 7x-3$ Divide both sides by $-6$ to isolate $y$ $y = {-\dfrac{7}{6}x + \dfrac{1}{2}}$ Substitute this expression for $y$ in the first equation. $-x-6({-\dfrac{7}{6}x + \dfrac{1}{2}}) = -3$ $-x + 7x - 3 = -3$ Simplify by combining terms, then solve for $x$ $6x - 3 = -3$ $6x = 0$ $x = 0$ Substitute $0$ for $x$ back into the top equation. $- 0-6y = -3$ $-6y = -3$ $-6y = -3$ $y = \dfrac{1}{2}$ The solution is $\enspace x = 0, \enspace y = \dfrac{1}{2}$.